Robust multiple beamforming massive mimo system based on cylindrical antenna arrays

This paper proposes a multiple beamforming system with robust optimum criteria to exploit the channel and minimize the inter-user interference among the cells. This system uses combined cylindrical array antenna multiple beamforming architecture with spatial multiplexing.

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ROBUST MULTIPLE BEAMFORMING MASSIVE MIMO SYSTEM

BASED ON CYLINDRICAL ANTENNA ARRAYS

Le Trung Tan1, Nguyen Huu Trung1*, Thai Trung Kien2

Abstract: The demand for high bit-rate service transmission is increasing for the

next generation of wireless systems such as the 5 th generation mobile communication system (5G) and digital video broadcasting-next generation handheld (DVB-NGH) Massive Multiple-input multiple-output (MIMO) transmission is one of the most promising techniques to fulfill this demand for high transmission rates It provides high diversity order, increased data-rate and high spectral efficiency This paper proposes a multiple beamforming system with robust optimum criteria to exploit the channel and minimize the inter-user interference among the cells This system uses combined cylindrical array antenna multiple beamforming architecture with spatial multiplexing The characteristics of the proposed system model is demonstrated using computer simulations under different criteria

Key words: Massive MIMO; Multiple-beamforming; Array antenna; Spatial multiplexing

I INTRODUCTION

The bandwidth-intensive immersive media services such as video services contribute a significant percent of data traffic in wireless networks Full high definition (Full HD) video is also being increasingly shared through social media such as YouTube, and 4K ultra HD (UHD) broadcasting is a short future [1-3] Massive Multiple-input multiple-output (MIMO) wireless systems employ a large number of transmit and receive antennas (usually greater than 100 elements), often called massive MIMO, have been of great interest in recent years because of their potential to dramatically improve spectral efficiency of future wireless systems and increase the transmission data rate through spatial multiplexing to deliver multiple streams of data within the same resource block (time and frequency) [4] Massive MIMO systems exploit multipath propagation to improve system reliability in terms of bit error rate (BER) performance, without the expense of additional bandwidth [5] Moreover, massive MIMO, by beamforming method, can increase the power efficiency by scaling down the transmit power of each terminal inversely proportional to the number of elements of antenna array at base stations [6] It can steer multiple beams to a number of user ends to enhance SNR ration

Orthogonal frequency division multiplexing (OFDM) is becoming the chosen modulation technique for wireless communications [7] OFDM can provide large data rates with sufficient robustness to radio channel impairments OFDM can provide large data rates with sufficient robustness to radio channel impairments These advantages make Massive MIMO a promising solution to achieve a higher data rate for future wireless systems especially when combined with the benefits of orthogonal frequency-division multiplexing (OFDM) [8]

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Công nghệ thông tin

L T Tan, N H Trung, T T Kien, “Robust multiple … cylindrical antenna arrays.”

84

Multiple beamforming is a technique that uses antenna arrays to produce a number of simultaneously available adjustable radiation patterns, which can point

to the desired coverage areas and minimize the impact of unwanted noise and interference, thereby improving the quality of desired signal Basically, beamforming if an optimal spatial filter [9] Antenna arrays using a beamforming technique can eliminate interferers having a direction of arrival different from that

of a desired signal Multi-polarized arrays can also eliminate undesired signals having different polarization from the desired signal, even if the signals have the same direction of arrival To increase the bandwidth, the mmWave frequencies in 5G systems require appropriate beamforming method [10-12]

The Base station (BTS) of wireless systems such as 4G, LTE, DVB-T contains

RF transceivers that are connected to the antennae The base stations have three or six-sector deployments An array of RF transceivers and antenna elements allows electronic baseband control of phase and amplitude to shape and steer the radiated beam [13]

For sectored configuration, BTS usually uses standard dual polarized antenna for MIMO The basic antenna consists of an array of dual polarization columns For example, 4x4 MIMO antenna for each sector has 8 columns and 4

RF connectors to form 4 separate beams The disadvantage of this system is the fixed structure for each sector The number of antenna elements for each beam

is fixed [14]

In this paper, in order to create a large angular coverage with good radiation pattern characteristics, the ability to change the number of antenna elements for each sector adapt to the number of users in that direction, we propose a multiple beamforming system with robust optimum criteria to exploit the channel and minimize the inter-user interference among the cells This system uses combined cylindrical array antenna multiple beamforming architecture with spatial multiplexing The resulted narrow beam width enhances the SNR ration, therefore the capacity is increased

The rest of the paper is organized as follows In the next section, the proposed system model is introduced Section III presents simulation results Concluding remarks and directions for further researches are mentioned in the last section

II SYSTEM MODEL 2.1 Signal model

Beamformers use an array of antenna elements that are individually phased in such a way as to form beams (or nulls) in a desired direction Typical beamforming antennas have highly correlated, closely spaced elements and columns Figure 1 describes a wireless connection between a centralized sectorized base stations and

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numerous fixed or nomadic users The base station is capable of generating a number of beams

Let us consider a multiple beamforming system with cylindrical equispaced

array antenna The inter-element distance is d The system has M elements per ring and the number of ring for multiple beamforming is N The number of element is

The system model is illustrated on Fig 2 Denote s(t) is transmitted signal of an arbitrary beam, the pointing angle associated with s(t) is , vector of array transmitting from N t elements at time instant t is expressed as :

Where ( , ) is steering vector

With is the carrier frequency and c is the speed of light Steering vector

depends on the direction of departure and the frequency For simplicity, we denote

( , ) is a The single beamforming model is expressed as ( ) = ( )

The multiple beamforming model is expressed as:

Where = [ ( , ), ( , ), … ( , )] according to P beams

There are two general beamforming systems, including narrow band beamforming and broad band beamforming In narrow band beamforming model,

the output signal of beamformer at time instant t is ( ) obtained by linear

combination of signals of elements as:

For broadband model, the output signal is expressed as [15]:

With − 1 is number of delay stages at each channel of ith element of the array The trasmitted signal is expressed as:

Where is the signal vector Vector of length represents the weights as:

The response of single beamformer is expressed as:

The beampattern is defined as squared magnitude of ( , ) Note that each of

weight in vector w impacts to the response of beamformer in terms of time and

space

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Output power or variance of estimated signal is determined as:

statistical independent over time Although signal statistic is not often stationary, but we design and evaluate the performance of optimized beamforming based on the hypothesis that the signal is wide sense stationary

2.2 Channel model

Figure 1 Cylindrical array antenna based multiple beamforming scenario

For each beam, the massive MIMO channel model is as follows:

⎣

⎢

ℎ ,

⋮

ℎ ,

⎥

⎤

In the matrix format:

Where = , , … , is a set of signals received from N R receive antennas of mobile station Because MIMO spatial multiplexing system takes advantage of transmit diversity in space over time caused by fading and multipath

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combined with signal orthogonalization The signal detection in the receiver is sequence detection Therefore, for sequence detection procedure, we set up signals

and channels as follows: Suppose that data is divided into blocks including K symbols In each block, to avoid inter block interference, we insert P vector zero containing N elements and N is the number of useful data samples with K = N + P

The channel is Finite Impulse Response fading channel (FIR) having L multipath

on each link from one transmit antenna to one receive antenna Choose P to satisfy

≥ − 1 Signal received at the jth

receive antenna in discrete time domain is of the form:

Where, [ ] is the signal sample received at the jth antenna at the discrete time

k vector [ ]= [ ], [ ], … , [ ] is output vector at the time k with

= 0,1, … , − 1 being elements of received vector = ( [0], [1], … , [ −

1 ; ℎ , is the lth element of the channel response , where l = 0, 1,… L – 1; transmitted signal vector at time k [ ]= [ ], [ ], … , [ ] ; The noise that affects the received signal samples is [ ] = [ ], [ ], … , [ ] ; The transmitted signal vector = ( [0], [1], … , [ − 1]) ; The AWGN noise vector = ( [0], [1], … , [ − 1])

The channel matrix H can be parameterized as [16]

Where = 1⁄ is is a normalization factor, is the complex gain of the

each path , are the azimuth and elevation angle of arrival or departure of the l-th path at the p-th cluster, respectively Λ ( , ) and Λ ( , ) represent the antenna element gain for the transmitter and receiver, respectively ( , ) and ( , ) represent the steering vector of the receiver and transmitter antenna array, respectively

We assume that the antenna elements are isotropic elements and there is no inter-element coupling/interference between elements The gain functions are equal unit, e.g Λ , = Λ , = 1 However, the isotropic elements could

be replaced by other antenna types such as patch antennas, etc., taking into account the corresponding gain functions

2.3 Optimum beamforming for proposed multiple beamforming system

The proposed multiple beamforming system functional block diagram is

presented in Figure 2 The beamformer function splits the RF signal into P beams

to feed each active element of the phased array It performs high-resolution phase

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and amplitude weighting, which is needed to synthesize beamforming patterns and adaptively null potential interferers The signal processing blocks for OFDM modulation include ITTF, P/S (parallel to serial), CP (c

DAC to form output signal The mixer converts the baseband signal up to carrier frequency

efficiency transmit PA, a transmit/receive switch, and low

optimize desired signal while minimizing interferences Statistically optimal beamforming techniqu

Error, MMSE, Linearly Constrained Minimum Variance, LCMV, minimum variance distortionless response, MVDR are widely applied [17] Design of the beamformer

the source and the statistical characteristics of the channel The optimum criteria are described as follow

2.3.1 Maximization of SNR

covariance matrices of signal and noise Depending on applications, the calculation

of

signal,

88

Figure 2.

The final block is the front

Beamforming is an important technique in array processing in order to optimize desired signal while minimizing interferences Statistically optimal beamforming techniqu

The weight vector is solution of maximization of

General solution

of

signal,

Figure 2.

General solution

covariance matrices of signal and noise Depending on applications, the calculation and

signal,

Figure 2.

General solution

signal,

L T Tan, N H Trung, T T Kien, “Robust multiple … cylindrical antenna arrays.

Figure 2.

General solution

is estimated from signal and known DOA by equation (10) We have,

DAC to form output signal The mixer converts the baseband signal up to carrier

Figure 2 Proposed multiple beamforming system functional block diagram

Error, MMSE, Linearly Constrained Minimum Variance, LCMV, minimum variance distortionless response, MVDR are widely applied [17] Design of the

under statistically optimal method requires statistical properties of the source and the statistical characteristics of the channel The optimum criteria are described as follow

General solution

are different

Proposed multiple beamforming system functional block diagram

General solution

are different

General solution

are different

Beamforming is an important technique in array processing in order to optimize desired signal while minimizing interferences Statistically optimal beamforming techniques include maximization of SNR,

are different

Beamforming is an important technique in array processing in order to optimize desired signal while minimizing interferences Statistically optimal

es include maximization of SNR, Error, MMSE, Linearly Constrained Minimum Variance, LCMV, minimum variance distortionless response, MVDR are widely applied [17] Design of the

under statistically optimal method requires statistical properties of the source and the statistical characteristics of the channel The optimum criteria

are different

=

are different For example,

= arg requires both covariance matrices of signal and noise Depending on applications, the calculation

For example,

The final block is the front-end, which contains a high

argmax requires both covariance matrices of signal and noise Depending on applications, the calculation

For example,

end, which contains a high efficiency transmit PA, a transmit/receive switch, and low

max requires both covariance matrices of signal and noise Depending on applications, the calculation

For example,

max requires both covariance matrices of signal and noise Depending on applications, the calculation

For example,

requires both covariance matrices of signal and noise Depending on applications, the calculation

For example,

requires both covariance matrices of signal and noise Depending on applications, the calculation

= covariance matrices of signal and noise Depending on applications, the calculation

can be estimated during absence of

The weight vector is solution of maximization of SNR problem:

{ covariance matrices of signal and noise Depending on applications, the calculation

SNR problem:

and amplitude weighting, which is needed to synthesize beamforming patterns and adaptively null potential interferers The signal processing blocks for OFDM modulation include ITTF, P/S (parallel to serial), CP (cyclic prefix insert) and DAC to form output signal The mixer converts the baseband signal up to carrier

end, which contains a high efficiency transmit PA, a transmit/receive switch, and low-noise amplifier (LNA) Beamforming is an important technique in array processing in order to optimize desired signal while minimizing interferences Statistically optimal

Minimum Mean Squared Error, MMSE, Linearly Constrained Minimum Variance, LCMV, minimum variance distortionless response, MVDR are widely applied [17] Design of the

SNR problem:

{ } and covariance matrices of signal and noise Depending on applications, the calculation

and amplitude weighting, which is needed to synthesize beamforming patterns and adaptively null potential interferers The signal processing blocks for OFDM

yclic prefix insert) and DAC to form output signal The mixer converts the baseband signal up to carrier

end, which contains a high

noise amplifier (LNA) Beamforming is an important technique in array processing in order to optimize desired signal while minimizing interferences Statistically optimal

SNR problem:

} and covariance matrices of signal and noise Depending on applications, the calculation

Công ngh

end, which contains a high-power and

noise amplifier (LNA) Beamforming is an important technique in array processing in order to optimize desired signal while minimizing interferences Statistically optimal

SNR problem:

and covariance matrices of signal and noise Depending on applications, the calculation

Công ngh

power and noise amplifier (LNA) Beamforming is an important technique in array processing in order to optimize desired signal while minimizing interferences Statistically optimal

SNR problem:

Công ngh

ệ thông tin

high noise amplifier (LNA) Beamforming is an important technique in array processing in order to optimize desired signal while minimizing interferences Statistically optimal

(15)

ệ thông tin

high-noise amplifier (LNA) Beamforming is an important technique in array processing in order to optimize desired signal while minimizing interferences Statistically optimal

(15) } are covariance matrices of signal and noise Depending on applications, the calculation

ệ thông tin

”

-Beamforming is an important technique in array processing in order to optimize desired signal while minimizing interferences Statistically optimal

(15) } are covariance matrices of signal and noise Depending on applications, the calculation

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multiplying the weight vector by a scale is not changing SNR Because steering vector ( , ) is fixed for a fixed signal, choose a weight vector to satisfy

( , ) = with c is a constant The problem of SNR maximization becomes

minimizing interference:

Using the method of Lagrange multipliers, solution of the equation [18]:

(17)

2.3.2 Minimum Mean Squared Error, MMSE

Minimum Mean Squared Error method minimizes the error signal between

transmitted signal and a reference signal d(t) In this model, desired user assumes

to transmit this reference signal, i.e ( )= α ( ) where α is amplitude of

reference signal d(t) and d(t) is known at the receiver The output signal of the

beamformer is to track reference signal [19] MMSE method seeks the weight to minimize average error signal power:

The average error signal power:

∗2

Where = { ∗}

| ( )|

We have the solution:

This solution is known as optimal Wiener filter This method requires reference signal to train the beamformer

2.3.3 Linearly Constrained Minimum Variance LCMV

LCMV method belongs to minimization of output power of the beamformer

desired signal fixed in order to preserve desired signal while minimizing the impact of undesired components including noise and interference that come from other directions other than desired direction

We have the output response of signal source with direction of arrival and frequency is determined by ( , ) Linear constraint for the weighs satisfies ( , ) = , where c is a constant to ensure that all signals with

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90

frequency come from direction of arrival are passed with response c

Minimization of output due to interference is equipvalent to minimizing the output power (minimum ouput power):

= arg min {| | } = arg min{ }, s.t ( , ) = (22)

Using the method of Lagrange multipliers, find min[ ( ; λ)]

Where:

Solution of the equation:

In practice, uncorrelated noise component ensures is invertible If c = 1 the

beamformer is called minimum variance distortionless response, MVDR, beamformer Solution of MVDR beamformer is equipvalent to maximization of SNR solution by replacing ( , ) ( , ) + by and applying invert

III NUMERICAL RESULTS

In this section, we provide simulation results to compare the proposed multiple beamforming system with cylindrical array antenna and present the total achievable capacity of the system for the proposed system

The performance of the system is performed by means of the Monte-Carlo simulation The Monte-Carlo simulation algorithm includes serial steps: Set up system configuration; create user data; MIMO precoding; create OFDM symbols; insert CP; create beamforming; receive signals; equalize MIMO; equalize MUD; demodulate OFDM, compare with source data, calculate BER The last estimate is

calculated as the average of all Q measured values after each simulation Bit error

rate BER is used to define the performance of the system

The system performance in simulation is Normalized Root Mean Square Error, NRMSE, the final value is the average value of all Q values after each simulation:

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In the simulation, the configuration of array is cylindrical array with number of Massive MIMO antennas is 200 to veify the performance after SNR, the distance

between two consecutive antenna elements is λ⁄2 Simulated signal has frequency f c

= 20 GHz, N = 10000 snapshots

Table 1 Simulation parameters

Sample resolution and beamforming

weight

bit 32 (complex double)

The simulation results are presented in Figure 3 (a-d) according to SNR ranges providing NRMSE of proposed system for MVDR, LCMV and FrostBeamformer algorithms The FrostBeamformer shows the best performance

among beamforming algorithms

(a) (b)

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92

(c) (d)

Figure 3 NRMSE according to SNR (a,b), number of antennas (c,d) of the

proposed massive MIMO system

(a) (b)

(c) (d)

Figure 4 Plot of array factor with 200-element Cylindrical Array; dual beam (a,b)

and single beam (c) of the proposed massive MIMO system

Figure 4 represents array factor in cases of single beamforming and multiple beamforming schemes, the number of elements is 200, SNR = 0dB, one interferer with INR = 0dB, carrier frequency is 20GHz Figure 4 (a), (b) presents MVDR

0.2 0.4 0.6 0.8 1

30

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240 90

270

120

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330

Angle [degree]

0 20 40 60 80 100 120 140 160 180 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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